document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162575>Question 1162575</A>: <I><SPAN STYLE=\"word-break: break-all;\"> . Suppose you own a car that is 40 months old. From an automobile dealer’s “Blue Book” you find that its trade-in value is SR3200. From an old Blue Book you find that its trade-in value 10 months ago was SR4700.<BR>\n" );
document.write( " a. Write a function expressing trade-in value as a function of the cars age in months.<BR>\n" );
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document.write( " b. You plan to get rid of the car when its trade-in value drops to SR1000. How much longer should you keep the car?<BR>\n" );
document.write( "c. What does the slope of your function represent in the real world? Why is it negative?<BR>\n" );
document.write( "d. When do you predict that car will be worthless? How do you know this?<BR>\n" );
document.write( "e. According to your model, what was the trade-in value of the car when it was new? <BR>\n" );
document.write( "f. Graph the function.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #786440 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=786440\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equation i used is y = mx + b<BR>\n" );
document.write( "this is a straight line depreciation equation.<BR>\n" );
document.write( "m is the slope<BR>\n" );
document.write( "b is the y-intercept<BR>\n" );
document.write( "2 points on this equation are known.<BR>\n" );
document.write( "they are (30,4700) and (40,3200)<BR>\n" );
document.write( "these points are in (x,y) format where x is the number of months and y is he value of the car.<BR>\n" );
document.write( "the slope is found by the equation of (y2-y1)/(x2-x1)<BR>\n" );
document.write( "assign (30,4700) to (x1,y1) and assign 40,3200 to (x2,y2) and replace those values in the slope equation to get:<BR>\n" );
document.write( "(3200 - 4700) / (40 - 30) = -1500 / 10 = -150<BR>\n" );
document.write( "m is equal to -150 and the equation the becomes y = -150x + b<BR>\n" );
document.write( "to solve for b, replace x and y with one of tghe coordinate points to get:<BR>\n" );
document.write( "4700 = -150 * 30 + b<BR>\n" );
document.write( "simplify and solve for b to get:<BR>\n" );
document.write( "b = 4700 + 4500 = 9200<BR>\n" );
document.write( "this makes the equation y = -150 * x + 9200 *****\r<BR>\n" );
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document.write( "answers to your questions are shown below:\r<BR>\n" );
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document.write( "a. Write a function expressing trade-in value as a function of the cars age in months.\r<BR>\n" );
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document.write( "y = -150 * x + 9200\r<BR>\n" );
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document.write( "y represents the value of the car and x represents the age of the car in months.\r<BR>\n" );
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document.write( "b. You plan to get rid of the car when its trade-in value drops to SR1000. How much longer should you keep the car?\r<BR>\n" );
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document.write( "replace y with 1000 in the equation to get:<BR>\n" );
document.write( "1000 = -150 * x + 9200<BR>\n" );
document.write( "subtract 1000 from both sides of the equation and add 150 * x to both sides of the equation and combine like terms to get:<BR>\n" );
document.write( "150 * x = 8200<BR>\n" );
document.write( "solve for x to get x = 8200 / 150 = 54.667 months rounded to 3 decimal places.\r<BR>\n" );
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document.write( "c. What does the slope of your function represent in the real world? Why is it negative?\r<BR>\n" );
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document.write( "the slope indicates that the value of the car is dropping by an average of 150 dollars for each additional month in the age of the car.\r<BR>\n" );
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document.write( "the slope is negative because the value of the car is dropping by that amount each month, on average.\r<BR>\n" );
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document.write( "d. When do you predict that car will be worthless? How do you know this?\r<BR>\n" );
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document.write( "set y = 0 to get 0 = -150 * x + 9200<BR>\n" );
document.write( "add 150 * x to both sides of the equation to get:<BR>\n" );
document.write( "150 * x = 9200<BR>\n" );
document.write( "divide both sides of the equation by 150 and solve for x to get:<BR>\n" );
document.write( "x = 9200 / 150 = 61.333 months rounded to 3 decimal places.\r<BR>\n" );
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document.write( "e. According to your model, what was the trade-in value of the car when it was new?\r<BR>\n" );
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document.write( "based oan the equation, the trade-in value of the car when it was new was 9200.\r<BR>\n" );
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document.write( "f. Graph the function.\r<BR>\n" );
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